1. Field of the Invention
The present invention relates to an error calculation method for an angle detection device.
2. Description of Related Art
A typically-known angle detection device is formed in the shape of a disk and includes: a graduation plate with a plurality of graduation lines provided radially from the center toward the circumference thereof; and a detector that detects the graduation lines. The angle detection device is configured to detect the rotation angle of the graduation plate based on an angle detected by the detector (see, for instance, Document 1, JP-A-07-140844).
An encoder device (angle detection device) disclosed in Document 1 includes: a circular plate (graduation plate) with a detectable portion (graduation lines); and two sensor members (detectors), in which the sensors are disposed at symmetrical positions relative to the rotation center of the circular plate. The encoder device calculates the average of angles detected by the sensor members to calculate the rotation angle of the circular plate.
FIG. 8A schematically shows a graduation plate 101 and FIG. 8B schematically shows detectors 102. FIG. 9 schematically shows an angle detection device 10.
As shown in FIGS. 8A, 8B and 9, the angle detection device 10 includes: a graduation plate 101 with a plurality of graduation lines 101A; and two detectors 102 disposed along the circumference of the graduation plate 101, the detectors 102 detecting the graduation lines 101A, in which the rotation angle of the graduation plate 101 is detected based on angles detected by the detectors 102.
In the angle detection device 10, as shown in FIG. 9, an error (hereinafter referred to as a center error) can be generated between a center O of the detectors 102 and a center O′ of the graduation plate 101 as a result of assembling, attachment to an object, a change in the temperature, or the like, which eventually leads to an error in the detected rotation angle of the graduation plate 101 (hereinafter referred to as an angle error).
Since the encoder device disclosed in Document 1 calculates the average of angles detected by the sensor members to detect the rotation angle of the circular plate, the angle error can be reduced.
However, as shown by the broken line in FIG. 9, the center O′ of the graduation plate 101 may rotate along with the rotation of the graduation plate 101.
The encoder device disclosed in Document 1 cannot reduce the angle error.
FIGS. 10A and 10B show the results of simulation of the relationship between the detected angle of the angle detection device 10 and the rotation angle of the graduation plate 101. FIG. 10A is a graph where the detected angle is represented by the vertical axis and the rotation angle of the graduation plate 101 is represented by the horizontal axis. FIG. 10B is a graph where the angle error is represented by the vertical axis and the rotation angle of the graduation plate 101 is represented by the horizontal axis.
The simulation was performed under the condition that the middle point in a straight line connecting the detectors 102 is defined as the center O of the detectors 102, the center O′ of the graduation plate 101 moves on the circumference of a circle with a radius equal to a center error δ along with the rotation of the graduation plate 101, and the angle detection device 10 has no error except the center error δ.
Without the center error δ, the angle detected by the angle detection device 10 is coincident with the rotation angle of the graduation plate 101 as shown by the broken line in FIG. 10A. However, if the center error δ occurs, an angle error is generated between the detected angle and the rotation angle of the graduation plate 101 as shown in the solid line in FIG. 10A. Specifically, as shown in FIG. 10B, the angle error is generated at the same frequency as the rotation of the graduation plate 101.
FIG. 11 shows the relationship between a rotation angle θ of the graduation plate 101 and detected angles θA1, θA2 of the detectors 102. Incidentally, in FIG. 11, a cartesian coordinate system with its origin at the center O of the detectors 102 is defined, in which an axis connecting the detectors 102 is defined as the X-axis and an axis orthogonal to the X-axis is defined as the Y-axis. The center O′ of the graduation plate 101 assumably exists on the X-axis before the rotation of the graduation plate 101 so that a cartesian coordinate system with its origin at the center O′ of the graduation plate 101 is defined. An axis set in the X-axis direction before the rotation of the graduation plate 101 is defined as an XE-axis and an axis orthogonal to the XE-axis is set as a YE-axis.
In FIG. 11, the detector 12 on the right side is denoted as 102A1 and the detector 12 on the left side is denoted as 102A2.
As shown in FIG. 11, when the graduation plate 101 rotates by the rotation angle θ, the detected angle θA1 of the detector 102A1 is equal to an angle between the XE-axis and a straight line connecting the center O′ of the graduation plate 101 and the detector 102A1. The detected angle θA2 of the detector 102A2 is equal to an angle between a straight line connecting the center O of the detectors 102 and the center O′ of the graduation plate 101 and a straight line connecting the center O′ of the graduation plate 101 and the detector 102A2.
The detected angles θA1, θA2 of the detectors 102A1, 102A2, which respectively contain angle errors ΔθA1, ΔθA2 resulting from the center error δ, are represented by the following equations (1):θA1=θ+ΔθA1 θA2=θ+ΔθA2  (1)
In the encoder device disclosed in Document 1, the rotation angle θ of the graduation plate 101, which is calculated by calculating the average of the detected angles θA1, θA2 of the detectors 102A1, 102A2, is represented by the following equation (2):
                                                                                                              θ                                          A                      ⁢                                                                                          ⁢                      1                                                        +                                      θ                                          A                      ⁢                                                                                          ⁢                      2                                                                      2                            =                                                                    2                    ⁢                                                                                  ⁢                    θ                                    +                                      Δθ                                          A                      ⁢                                                                                          ⁢                      1                                                        +                                      Δθ                                          A                      ⁢                                                                                          ⁢                      2                                                                      2                                                                                        =                              θ                +                                                                            Δ                      ⁢                                                                                          ⁢                                              θ                                                  A                          ⁢                                                                                                          ⁢                          1                                                                                      +                                          Δθ                                              A                        ⁢                                                                                                  ⁢                        2                                                                              2                                                                                        (        2        )            
In other words, in order to calculate the rotation angle θ of the graduation plate 101 without any error, it is required that the following equation (3) is established:ΔθA1+ΔθA2=0  (3)
FIGS. 12A, 12B show the results of simulation of the angle errors ΔθA1, ΔθA2 when the center error δ is relatively large. FIGS. 13A, 13B show the results of simulation of the angle errors ΔθA1, ΔθA2 when the center error δ is relatively small. Incidentally, FIGS. 12A, 12B and FIGS. 13A, 13B are graphs in which the angle error is represented by the vertical axis and the rotation angle of the graduation plate 101 is represented by the horizontal axis. When the distance between the center O of the detectors 102 and the detectors 102 is set at 1, the center error δ is equal to 0.3 in the simulation of FIGS. 12A, 12B and the center error δ is equal to 0.003 in the simulation of FIGS. 13A, 13B.
The total of the angle errors ΔθA1, ΔθA2 does not become 0 irrespective of the amount of the center error δ as shown in FIGS. 12A, 12B and FIGS. 13A, 13B, and therefore the above equation (3) is not established.
Thus, when the center O′ of the graduation plate 101 rotates along with the rotation of the graduation plate 101, the angle error cannot be reduced without calculating the center error δ.